LMFDB - Embedded newform 400.3.bg.f.97.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,3,Mod(17,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 0, 13])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			97.2
Character	$\chi$	$=$	400.97
Dual form			400.3.bg.f.33.2

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.88880 + 0.615926i) q^{3} +(2.05707 - 4.55724i) q^{5} +(-5.11305 - 5.11305i) q^{7} +(6.18393 - 2.00928i) q^{9} +(0.0865225 - 0.266289i) q^{11} +(-5.04080 - 2.56841i) q^{13} +(-5.19263 + 18.9892i) q^{15} +(9.22052 + 1.46039i) q^{17} +(14.8832 + 20.4849i) q^{19} +(23.0329 + 16.7344i) q^{21} +(-11.5801 - 22.7271i) q^{23} +(-16.5369 - 18.7492i) q^{25} +(8.76274 - 4.46484i) q^{27} +(-26.1473 + 35.9887i) q^{29} +(-44.2788 + 32.1704i) q^{31} +(-0.172455 + 1.08884i) q^{33} +(-33.8193 + 12.7835i) q^{35} +(-17.6833 + 34.7055i) q^{37} +(21.1846 + 6.88330i) q^{39} +(5.93471 + 18.2652i) q^{41} +(-23.5671 + 23.5671i) q^{43} +(3.56401 - 32.3149i) q^{45} +(2.94533 + 18.5961i) q^{47} +3.28662i q^{49} -36.7563 q^{51} +(-49.6251 + 7.85985i) q^{53} +(-1.03556 - 0.942080i) q^{55} +(-70.4949 - 70.4949i) q^{57} +(73.1755 - 23.7762i) q^{59} +(-32.1545 + 98.9614i) q^{61} +(-41.8923 - 21.3452i) q^{63} +(-22.0742 + 17.6887i) q^{65} +(29.9952 + 4.75077i) q^{67} +(59.0308 + 81.2490i) q^{69} +(-18.4157 - 13.3798i) q^{71} +(-4.79456 - 9.40984i) q^{73} +(75.8569 + 62.7263i) q^{75} +(-1.80394 + 0.919155i) q^{77} +(71.4829 - 98.3877i) q^{79} +(-78.6699 + 57.1570i) q^{81} +(-4.05019 + 25.5719i) q^{83} +(25.6226 - 39.0160i) q^{85} +(79.5155 - 156.058i) q^{87} +(-19.5716 - 6.35919i) q^{89} +(12.6414 + 38.9063i) q^{91} +(152.377 - 152.377i) q^{93} +(123.970 - 25.6872i) q^{95} +(-23.4342 - 147.957i) q^{97} -1.82056i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39}+ \cdots - 544 q^{97}+O(q^{100}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{17}{20}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−3.88880	+	0.615926i	−1.29627	+	0.205309i	−0.766176	−	0.642631i	$-0.777843\pi$
$3$	−3.88880	+	0.615926i	−1.29627	+	0.205309i	−0.530093	+	0.847940i	$0.677843\pi$
$4$		0			0
$5$	2.05707	−	4.55724i	0.411414	−	0.911448i
$5$	2.05707	−	4.55724i	0.411414	−	0.911448i
$6$		0			0
$7$	−5.11305	−	5.11305i	−0.730436	−	0.730436i	0.240270	−	0.970706i	$-0.422764\pi$
$7$	−5.11305	−	5.11305i	−0.730436	−	0.730436i	−0.970706	+	0.240270i	$0.922764\pi$
$8$		0			0
$9$	6.18393	−	2.00928i	0.687103	−	0.223253i
$10$		0			0
$11$	0.0865225	−	0.266289i	0.00786568	−	0.0242081i	−0.947047	−	0.321096i	$-0.895949\pi$
$11$	0.0865225	−	0.266289i	0.00786568	−	0.0242081i	0.954912	+	0.296888i	$0.0959488\pi$
$12$		0			0
$13$	−5.04080	−	2.56841i	−0.387754	−	0.197570i	0.249236	−	0.968443i	$-0.419821\pi$
$13$	−5.04080	−	2.56841i	−0.387754	−	0.197570i	−0.636990	+	0.770872i	$0.719821\pi$
$14$		0			0
$15$	−5.19263	+	18.9892i	−0.346175	+	1.26595i
$16$		0			0
$17$	9.22052	+	1.46039i	0.542384	+	0.0859051i	0.421614	−	0.906775i	$-0.361464\pi$
$17$	9.22052	+	1.46039i	0.542384	+	0.0859051i	0.120770	+	0.992681i	$0.461464\pi$
$18$		0			0
$19$	14.8832	+	20.4849i	0.783324	+	1.07815i	0.994907	+	0.100793i	$0.0321381\pi$
$19$	14.8832	+	20.4849i	0.783324	+	1.07815i	−0.211583	+	0.977360i	$0.567862\pi$
$20$		0			0
$21$	23.0329	+	16.7344i	1.09681	+	0.796876i
$22$		0			0
$23$	−11.5801	−	22.7271i	−0.503481	−	0.988136i	−0.993218	−	0.116266i	$-0.962907\pi$
$23$	−11.5801	−	22.7271i	−0.503481	−	0.988136i	0.489737	−	0.871870i	$-0.337093\pi$
$24$		0			0
$25$	−16.5369	−	18.7492i	−0.661476	−	0.749966i
$26$		0			0
$27$	8.76274	−	4.46484i	0.324546	−	0.165365i
$28$		0			0
$29$	−26.1473	+	35.9887i	−0.901632	+	1.24099i	0.0683127	+	0.997664i	$0.478238\pi$
$29$	−26.1473	+	35.9887i	−0.901632	+	1.24099i	−0.969945	+	0.243326i	$0.921762\pi$
$30$		0			0
$31$	−44.2788	+	32.1704i	−1.42835	+	1.03776i	−0.438027	+	0.898962i	$0.644323\pi$
$31$	−44.2788	+	32.1704i	−1.42835	+	1.03776i	−0.990321	+	0.138794i	$0.955677\pi$
$32$		0			0
$33$	−0.172455	+	1.08884i	−0.00522591	+	0.0329951i
$34$		0			0
$35$	−33.8193	+	12.7835i	−0.966267	+	0.365243i
$36$		0			0
$37$	−17.6833	+	34.7055i	−0.477928	+	0.937987i	0.518623	+	0.855003i	$0.326445\pi$
$37$	−17.6833	+	34.7055i	−0.477928	+	0.937987i	−0.996551	+	0.0829838i	$0.973555\pi$
$38$		0			0
$39$	21.1846	+	6.88330i	0.543196	+	0.176495i
$40$		0			0
$41$	5.93471	+	18.2652i	0.144749	+	0.445492i	0.996979	−	0.0776760i	$-0.0247500\pi$
$41$	5.93471	+	18.2652i	0.144749	+	0.445492i	−0.852230	+	0.523168i	$0.824750\pi$
$42$		0			0
$43$	−23.5671	+	23.5671i	−0.548073	+	0.548073i	−0.925883	−	0.377810i	$-0.876677\pi$
$43$	−23.5671	+	23.5671i	−0.548073	+	0.548073i	0.377810	+	0.925883i	$0.376677\pi$
$44$		0			0
$45$	3.56401	−	32.3149i	0.0792003	−	0.718109i
$46$		0			0
$47$	2.94533	+	18.5961i	0.0626666	+	0.395661i	0.999006	+	0.0445663i	$0.0141906\pi$
$47$	2.94533	+	18.5961i	0.0626666	+	0.395661i	−0.936340	+	0.351095i	$0.885809\pi$
$48$		0			0
$49$			3.28662i			0.0670739i
$50$		0			0
$51$	−36.7563			−0.720712
$52$		0			0
$53$	−49.6251	+	7.85985i	−0.936323	+	0.148299i	−0.605906	−	0.795536i	$-0.707189\pi$
$53$	−49.6251	+	7.85985i	−0.936323	+	0.148299i	−0.330417	+	0.943835i	$0.607189\pi$
$54$		0			0
$55$	−1.03556	−	0.942080i	−0.0188284	−	0.0171287i
$56$		0			0
$57$	−70.4949	−	70.4949i	−1.23675	−	1.23675i
$58$		0			0
$59$	73.1755	−	23.7762i	1.24026	−	0.402986i	0.385841	−	0.922565i	$-0.373911\pi$
$59$	73.1755	−	23.7762i	1.24026	−	0.402986i	0.854422	+	0.519580i	$0.173911\pi$
$60$		0			0
$61$	−32.1545	+	98.9614i	−0.527123	+	1.62232i	0.232955	+	0.972487i	$0.425160\pi$
$61$	−32.1545	+	98.9614i	−0.527123	+	1.62232i	−0.760079	+	0.649831i	$0.774840\pi$
$62$		0			0
$63$	−41.8923	−	21.3452i	−0.664957	−	0.338813i
$64$		0			0
$65$	−22.0742	+	17.6887i	−0.339603	+	0.272134i
$66$		0			0
$67$	29.9952	+	4.75077i	0.447690	+	0.0709071i	0.376209	−	0.926535i	$-0.377228\pi$
$67$	29.9952	+	4.75077i	0.447690	+	0.0709071i	0.0714809	+	0.997442i	$0.477228\pi$
$68$		0			0
$69$	59.0308	+	81.2490i	0.855519	+	1.17752i
$70$		0			0
$71$	−18.4157	−	13.3798i	−0.259377	−	0.188448i	0.450496	−	0.892779i	$-0.351247\pi$
$71$	−18.4157	−	13.3798i	−0.259377	−	0.188448i	−0.709872	+	0.704330i	$0.751247\pi$
$72$		0			0
$73$	−4.79456	−	9.40984i	−0.0656788	−	0.128902i	0.855833	−	0.517252i	$-0.173045\pi$
$73$	−4.79456	−	9.40984i	−0.0656788	−	0.128902i	−0.921512	+	0.388350i	$0.873045\pi$
$74$		0			0
$75$	75.8569	+	62.7263i	1.01143	+	0.836350i
$76$		0			0
$77$	−1.80394	+	0.919155i	−0.0234278	+	0.0119371i
$78$		0			0
$79$	71.4829	−	98.3877i	0.904847	−	1.24541i	−0.0640496	−	0.997947i	$-0.520402\pi$
$79$	71.4829	−	98.3877i	0.904847	−	1.24541i	0.968896	−	0.247468i	$-0.0795984\pi$
$80$		0			0
$81$	−78.6699	+	57.1570i	−0.971233	+	0.705642i
$82$		0			0
$83$	−4.05019	+	25.5719i	−0.0487975	+	0.308095i	−1.00000		0.000472307i	$-0.999850\pi$
$83$	−4.05019	+	25.5719i	−0.0487975	+	0.308095i	0.951202	+	0.308568i	$0.0998497\pi$
$84$		0			0
$85$	25.6226	−	39.0160i	0.301443	−	0.459012i
$86$		0			0
$87$	79.5155	−	156.058i	0.913971	−	1.79377i
$88$		0			0
$89$	−19.5716	−	6.35919i	−0.219905	−	0.0714516i	0.196992	−	0.980405i	$-0.436883\pi$
$89$	−19.5716	−	6.35919i	−0.219905	−	0.0714516i	−0.416898	+	0.908953i	$0.636883\pi$
$90$		0			0
$91$	12.6414	+	38.9063i	0.138917	+	0.427542i
$92$		0			0
$93$	152.377	−	152.377i	1.63846	−	1.63846i
$94$		0			0
$95$	123.970	−	25.6872i	1.30495	−	0.270392i
$96$		0			0
$97$	−23.4342	−	147.957i	−0.241589	−	1.52533i	−0.748383	−	0.663267i	$-0.769169\pi$
$97$	−23.4342	−	147.957i	−0.241589	−	1.52533i	0.506793	−	0.862068i	$-0.330831\pi$
$98$		0			0
$99$		−	1.82056i		−	0.0183895i
$100$		0			0
$101$	−48.4125			−0.479332			−0.239666	−	0.970855i	$-0.577038\pi$
$101$	−48.4125			−0.479332			−0.239666	+	0.970855i	$0.577038\pi$
$102$		0			0
$103$	−120.042	+	19.0128i	−1.16546	+	0.184590i	−0.709035	−	0.705173i	$-0.750869\pi$
$103$	−120.042	+	19.0128i	−1.16546	+	0.184590i	−0.456422	+	0.889763i	$0.650869\pi$
$104$		0			0
$105$	123.643	−	70.5428i	1.17755	−	0.671836i
$106$		0			0
$107$	104.833	+	104.833i	0.979751	+	0.979751i	0.999799	−	0.0200477i	$-0.00638180\pi$
$107$	104.833	+	104.833i	0.979751	+	0.979751i	−0.0200477	+	0.999799i	$0.506382\pi$
$108$		0			0
$109$	136.885	−	44.4765i	1.25582	−	0.408041i	0.395818	−	0.918329i	$-0.370461\pi$
$109$	136.885	−	44.4765i	1.25582	−	0.408041i	0.860004	+	0.510287i	$0.170461\pi$
$110$		0			0
$111$	47.3910	−	145.855i	0.426946	−	1.31401i
$112$		0			0
$113$	122.130	+	62.2282i	1.08079	+	0.550692i	0.901357	−	0.433077i	$-0.142572\pi$
$113$	122.130	+	62.2282i	1.08079	+	0.550692i	0.179438	+	0.983769i	$0.442572\pi$
$114$		0			0
$115$	−127.394	+	6.02175i	−1.10777	+	0.0523631i
$116$		0			0
$117$	−36.3326	−	5.75452i	−0.310535	−	0.0491839i
$118$		0			0
$119$	−39.6780	−	54.6121i	−0.333428	−	0.458925i
$120$		0			0
$121$	97.8276	+	71.0759i	0.808493	+	0.587404i
$122$		0			0
$123$	−34.3289	−	67.3744i	−0.279097	−	0.547759i
$124$		0			0
$125$	−119.462	+	36.7943i	−0.955696	+	0.294355i
$126$		0			0
$127$	−108.864	+	55.4692i	−0.857200	+	0.436765i	−0.826616	−	0.562767i	$-0.809737\pi$
$127$	−108.864	+	55.4692i	−0.857200	+	0.436765i	−0.0305846	+	0.999532i	$0.509737\pi$
$128$		0			0
$129$	77.1324	−	106.164i	0.597925	−	0.822974i
$130$		0			0
$131$	−146.603	+	106.513i	−1.11911	+	0.813079i	−0.984073	−	0.177762i	$-0.943114\pi$
$131$	−146.603	+	106.513i	−1.11911	+	0.813079i	−0.135033	+	0.990841i	$0.543114\pi$
$132$		0			0
$133$	28.6421	−	180.839i	0.215354	−	1.35969i
$134$		0			0
$135$	−2.32176	−	49.1184i	−0.0171983	−	0.363840i
$136$		0			0
$137$	16.0731	−	31.5452i	0.117322	−	0.230257i	−0.824876	−	0.565313i	$-0.808755\pi$
$137$	16.0731	−	31.5452i	0.117322	−	0.230257i	0.942198	+	0.335056i	$0.108755\pi$
$138$		0			0
$139$	−54.9774	−	17.8632i	−0.395521	−	0.128513i	0.104502	−	0.994525i	$-0.466675\pi$
$139$	−54.9774	−	17.8632i	−0.395521	−	0.128513i	−0.500023	+	0.866012i	$0.666675\pi$
$140$		0			0
$141$	−22.9076	−	70.5024i	−0.162465	−	0.500017i
$142$		0			0
$143$	−1.12008	+	1.12008i	−0.00783275	+	0.00783275i
$144$		0			0
$145$	110.222	+	193.191i	0.760154	+	1.33235i
$146$		0			0
$147$	−2.02432	−	12.7810i	−0.0137709	−	0.0869458i
$148$		0			0
$149$			241.873i			1.62331i	0.584140	+	0.811653i	$0.301432\pi$
$149$			241.873i			1.62331i	−0.584140	+	0.811653i	$0.698568\pi$
$150$		0			0
$151$	−94.4994			−0.625824			−0.312912	−	0.949782i	$-0.601304\pi$
$151$	−94.4994			−0.625824			−0.312912	+	0.949782i	$0.601304\pi$
$152$		0			0
$153$	59.9534	−	9.49568i	0.391852	−	0.0620633i
$154$		0			0
$155$	55.5238	+	267.966i	0.358218	+	1.72881i
$156$		0			0
$157$	−187.357	−	187.357i	−1.19336	−	1.19336i	−0.976118	−	0.217241i	$-0.930294\pi$
$157$	−187.357	−	187.357i	−1.19336	−	1.19336i	−0.217241	−	0.976118i	$-0.569706\pi$
$158$		0			0
$159$	188.141	−	61.1308i	1.18328	−	0.384471i
$160$		0			0
$161$	−56.9956	+	175.415i	−0.354010	+	1.08953i
$162$		0			0
$163$	39.7438	+	20.2505i	0.243827	+	0.124236i	0.571634	−	0.820509i	$-0.306310\pi$
$163$	39.7438	+	20.2505i	0.243827	+	0.124236i	−0.327807	+	0.944745i	$0.606310\pi$
$164$		0			0
$165$	4.60734	+	3.02574i	0.0279233	+	0.0183378i
$166$		0			0
$167$	−234.821	−	37.1920i	−1.40612	−	0.222707i	−0.593184	−	0.805067i	$-0.702129\pi$
$167$	−234.821	−	37.1920i	−1.40612	−	0.222707i	−0.812931	+	0.582360i	$0.802129\pi$
$168$		0			0
$169$	−80.5228	−	110.830i	−0.476466	−	0.655800i
$170$		0			0
$171$	133.196	+	96.7728i	0.778926	+	0.565923i
$172$		0			0
$173$	−126.827	−	248.913i	−0.733107	−	1.43880i	−0.892247	−	0.451547i	$-0.850872\pi$
$173$	−126.827	−	248.913i	−0.733107	−	1.43880i	0.159140	−	0.987256i	$-0.449128\pi$
$174$		0			0
$175$	−11.3113	+	180.419i	−0.0646361	+	1.03097i
$176$		0			0
$177$	−269.921	+	137.532i	−1.52498	+	0.777014i
$178$		0			0
$179$	54.7109	−	75.3030i	0.305647	−	0.420687i	−0.628370	−	0.777914i	$-0.716278\pi$
$179$	54.7109	−	75.3030i	0.305647	−	0.420687i	0.934018	+	0.357227i	$0.116278\pi$
$180$		0			0
$181$	282.031	−	204.908i	1.55818	−	1.13209i	0.620703	−	0.784046i	$-0.286847\pi$
$181$	282.031	−	204.908i	1.55818	−	1.13209i	0.937479	−	0.348041i	$-0.113153\pi$
$182$		0			0
$183$	64.0897	−	404.646i	0.350217	−	2.21118i
$184$		0			0
$185$	121.786	+	151.979i	0.658300	+	0.821508i
$186$		0			0
$187$	1.18667	−	2.32897i	0.00634582	−	0.0124544i
$188$		0			0
$189$	−67.6333	−	21.9754i	−0.357848	−	0.116272i
$190$		0			0
$191$	−29.5335	−	90.8949i	−0.154626	−	0.475890i	0.843497	−	0.537134i	$-0.180493\pi$
$191$	−29.5335	−	90.8949i	−0.154626	−	0.475890i	−0.998123	+	0.0612445i	$0.980493\pi$
$192$		0			0
$193$	−45.2300	+	45.2300i	−0.234352	+	0.234352i	−0.814507	−	0.580154i	$-0.802992\pi$
$193$	−45.2300	+	45.2300i	−0.234352	+	0.234352i	0.580154	+	0.814507i	$0.302992\pi$
$194$		0			0
$195$	74.9472	−	82.3840i	0.384345	−	0.422482i
$196$		0			0
$197$	20.3420	+	128.434i	0.103259	+	0.651950i	0.983975	+	0.178306i	$0.0570617\pi$
$197$	20.3420	+	128.434i	0.103259	+	0.651950i	−0.880716	+	0.473644i	$0.842938\pi$
$198$		0			0
$199$			165.880i			0.833568i	0.909006	+	0.416784i	$0.136843\pi$
$199$			165.880i			0.833568i	−0.909006	+	0.416784i	$0.863157\pi$
$200$		0			0
$201$	−119.572			−0.594884
$202$		0			0
$203$	317.705	−	50.3195i	1.56505	−	0.247879i
$204$		0			0
$205$	95.4470	+	10.5268i	0.465595	+	0.0513505i
$206$		0			0
$207$	−117.275	−	117.275i	−0.566548	−	0.566548i
$208$		0			0
$209$	6.74263	−	2.19081i	0.0322614	−	0.0104824i
$210$		0			0
$211$	34.9729	−	107.635i	0.165748	−	0.510121i	−0.833342	−	0.552757i	$-0.813576\pi$
$211$	34.9729	−	107.635i	0.165748	−	0.510121i	0.999091	+	0.0426364i	$0.0135757\pi$
$212$		0			0
$213$	79.8562	+	40.6888i	0.374912	+	0.191027i
$214$		0			0
$215$	58.9218	+	155.880i	0.274055	+	0.725025i
$216$		0			0
$217$	390.889	+	61.9107i	1.80133	+	0.285303i
$218$		0			0
$219$	24.4409	+	33.6400i	0.111602	+	0.153607i
$220$		0			0
$221$	−42.7279	−	31.0436i	−0.193339	−	0.140469i
$222$		0			0
$223$	76.8865	+	150.898i	0.344782	+	0.676674i	0.996661	−	0.0816497i	$-0.0260189\pi$
$223$	76.8865	+	150.898i	0.344782	+	0.676674i	−0.651879	+	0.758323i	$0.726019\pi$
$224$		0			0
$225$	−139.935	−	82.7162i	−0.621935	−	0.367627i
$226$		0			0
$227$	−354.121	+	180.434i	−1.56001	+	0.794863i	−0.999447	−	0.0332522i	$-0.989414\pi$
$227$	−354.121	+	180.434i	−1.56001	+	0.794863i	−0.560559	+	0.828115i	$0.689414\pi$
$228$		0			0
$229$	108.078	−	148.756i	0.471955	−	0.649590i	−0.504979	−	0.863131i	$-0.668500\pi$
$229$	108.078	−	148.756i	0.471955	−	0.649590i	0.976934	+	0.213542i	$0.0684999\pi$
$230$		0			0
$231$	6.44905	−	4.68551i	0.0279180	−	0.0202836i
$232$		0			0
$233$	−45.9121	+	289.878i	−0.197048	+	1.24411i	0.668663	+	0.743566i	$0.266867\pi$
$233$	−45.9121	+	289.878i	−0.197048	+	1.24411i	−0.865711	+	0.500545i	$0.833133\pi$
$234$		0			0
$235$	90.8056	+	24.8309i	0.386407	+	0.105663i
$236$		0			0
$237$	−217.383	+	426.639i	−0.917229	+	1.80016i
$238$		0			0
$239$	−17.8751	−	5.80798i	−0.0747913	−	0.0243012i	0.271382	−	0.962472i	$-0.412519\pi$
$239$	−17.8751	−	5.80798i	−0.0747913	−	0.0243012i	−0.346174	+	0.938170i	$0.612519\pi$
$240$		0			0
$241$	−107.483	−	330.799i	−0.445989	−	1.37261i	−0.881396	−	0.472378i	$-0.843396\pi$
$241$	−107.483	−	330.799i	−0.445989	−	1.37261i	0.435408	−	0.900233i	$-0.356604\pi$
$242$		0			0
$243$	208.140	−	208.140i	0.856543	−	0.856543i
$244$		0			0
$245$	14.9779	+	6.76082i	0.0611344	+	0.0275952i
$246$		0			0
$247$	−22.4092	−	141.486i	−0.0907257	−	0.572819i
$248$		0			0
$249$		−	101.939i		−	0.409393i
$250$		0			0
$251$	−358.291			−1.42746			−0.713728	−	0.700423i	$-0.752995\pi$
$251$	−358.291			−1.42746			−0.713728	+	0.700423i	$0.752995\pi$
$252$		0			0
$253$	−7.05392	+	1.11723i	−0.0278811	+	0.00441593i
$254$		0			0
$255$	−75.6104	+	167.507i	−0.296511	+	0.656892i
$256$		0			0
$257$	−93.9152	−	93.9152i	−0.365429	−	0.365429i	0.500378	−	0.865807i	$-0.333194\pi$
$257$	−93.9152	−	93.9152i	−0.365429	−	0.365429i	−0.865807	+	0.500378i	$0.833194\pi$
$258$		0			0
$259$	267.867	−	87.0353i	1.03424	−	0.336044i
$260$		0			0
$261$	−89.3818	+	275.089i	−0.342459	+	1.05398i
$262$		0			0
$263$	−32.3684	−	16.4925i	−0.123074	−	0.0627092i	0.391370	−	0.920234i	$-0.372001\pi$
$263$	−32.3684	−	16.4925i	−0.123074	−	0.0627092i	−0.514443	+	0.857524i	$0.672001\pi$
$264$		0			0
$265$	−66.2633	+	242.322i	−0.250050	+	0.914423i
$266$		0			0
$267$	80.0269	+	12.6750i	0.299726	+	0.0474719i
$268$		0			0
$269$	−126.562	−	174.198i	−0.470491	−	0.647575i	0.506152	−	0.862444i	$-0.331068\pi$
$269$	−126.562	−	174.198i	−0.470491	−	0.647575i	−0.976643	+	0.214869i	$0.931068\pi$
$270$		0			0
$271$	152.245	+	110.612i	0.561789	+	0.408164i	0.832113	−	0.554606i	$-0.187131\pi$
$271$	152.245	+	110.612i	0.561789	+	0.408164i	−0.270324	+	0.962769i	$0.587131\pi$
$272$		0			0
$273$	−73.1234	−	143.513i	−0.267851	−	0.525688i
$274$		0			0
$275$	−6.42351	+	2.78137i	−0.0233582	+	0.0101141i
$276$		0			0
$277$	−181.467	+	92.4618i	−0.655114	+	0.333797i	−0.749756	−	0.661714i	$-0.769829\pi$
$277$	−181.467	+	92.4618i	−0.655114	+	0.333797i	0.0946423	+	0.995511i	$0.469829\pi$
$278$		0			0
$279$	−209.178	+	287.908i	−0.749740	+	1.03193i
$280$		0			0
$281$	−259.573	+	188.591i	−0.923747	+	0.671142i	−0.944454	−	0.328644i	$-0.893408\pi$
$281$	−259.573	+	188.591i	−0.923747	+	0.671142i	0.0207066	+	0.999786i	$0.493408\pi$
$282$		0			0
$283$	16.3976	−	103.531i	0.0579422	−	0.365833i	−0.941632	−	0.336645i	$-0.890708\pi$
$283$	16.3976	−	103.531i	0.0579422	−	0.365833i	0.999574	−	0.0291880i	$-0.00929215\pi$
$284$		0			0
$285$	−466.275	+	176.249i	−1.63605	+	0.618418i
$286$		0			0
$287$	63.0463	−	123.735i	0.219673	−	0.431134i
$288$		0			0
$289$	−191.970	−	62.3748i	−0.664256	−	0.215830i
$290$		0			0
$291$	182.262	+	560.944i	0.626329	+	1.92764i
$292$		0			0
$293$	−60.8637	+	60.8637i	−0.207726	+	0.207726i	−0.803300	−	0.595574i	$-0.796925\pi$
$293$	−60.8637	+	60.8637i	−0.207726	+	0.207726i	0.595574	+	0.803300i	$0.296925\pi$
$294$		0			0
$295$	42.1736	−	382.388i	0.142961	−	1.29623i
$296$		0			0
$297$	−0.430763	−	2.71973i	−0.00145038	−	0.00915735i
$298$		0			0
$299$			144.305i			0.482626i
$300$		0			0
$301$	241.000			0.800665
$302$		0			0
$303$	188.267	−	29.8185i	0.621343	−	0.0984110i
$304$		0			0
$305$	384.847	+	350.107i	1.26179	+	1.14789i
$306$		0			0
$307$	−382.682	−	382.682i	−1.24652	−	1.24652i	−0.957246	−	0.289274i	$-0.906586\pi$
$307$	−382.682	−	382.682i	−1.24652	−	1.24652i	−0.289274	−	0.957246i	$-0.593414\pi$
$308$		0			0
$309$	455.110	−	147.874i	1.47285	−	0.478557i
$310$		0			0
$311$	13.8868	−	42.7392i	0.0446521	−	0.137425i	−0.926245	−	0.376922i	$-0.876982\pi$
$311$	13.8868	−	42.7392i	0.0446521	−	0.137425i	0.970897	+	0.239497i	$0.0769825\pi$
$312$		0			0
$313$	−2.01992	−	1.02920i	−0.00645342	−	0.00328818i	0.450761	−	0.892645i	$-0.351153\pi$
$313$	−2.01992	−	1.02920i	−0.00645342	−	0.00328818i	−0.457214	+	0.889357i	$0.651153\pi$
$314$		0			0
$315$	−183.451	+	147.005i	−0.582383	+	0.466682i
$316$		0			0
$317$	157.199	+	24.8979i	0.495896	+	0.0785422i	0.399373	−	0.916789i	$-0.369228\pi$
$317$	157.199	+	24.8979i	0.495896	+	0.0785422i	0.0965228	+	0.995331i	$0.469228\pi$
$318$		0			0
$319$	7.32106	+	10.0766i	0.0229500	+	0.0315880i
$320$		0			0
$321$	−472.246	−	343.107i	−1.47117	−	1.06887i
$322$		0			0
$323$	107.315	+	210.617i	0.332243	+	0.652064i
$324$		0			0
$325$	35.2036	+	136.984i	0.108319	+	0.421490i
$326$		0			0
$327$	−504.923	+	257.271i	−1.54411	+	0.786762i
$328$		0			0
$329$	80.0231	−	110.142i	0.243231	−	0.334779i
$330$		0			0
$331$	−251.942	+	183.047i	−0.761155	+	0.553011i	−0.899264	−	0.437406i	$-0.855897\pi$
$331$	−251.942	+	183.047i	−0.761155	+	0.553011i	0.138110	+	0.990417i	$0.455897\pi$
$332$		0			0
$333$	−39.6194	+	250.147i	−0.118977	+	0.751193i
$334$		0			0
$335$	83.3527	−	126.923i	0.248814	−	0.378874i
$336$		0			0
$337$	280.615	−	550.737i	0.832684	−	1.63423i	0.0610793	−	0.998133i	$-0.480546\pi$
$337$	280.615	−	550.737i	0.832684	−	1.63423i	0.771605	−	0.636102i	$-0.219454\pi$
$338$		0			0
$339$	−513.267	−	166.770i	−1.51406	−	0.491948i
$340$		0			0
$341$	4.73552	+	14.5744i	0.0138871	+	0.0427402i
$342$		0			0
$343$	−233.735	+	233.735i	−0.681443	+	0.681443i
$344$		0			0
$345$	491.702	−	101.883i	1.42522	−	0.295312i
$346$		0			0
$347$	60.4828	+	381.874i	0.174302	+	1.10050i	0.907366	+	0.420341i	$0.138089\pi$
$347$	60.4828	+	381.874i	0.174302	+	1.10050i	−0.733064	+	0.680159i	$0.761911\pi$
$348$		0			0
$349$			324.359i			0.929396i	0.885469	+	0.464698i	$0.153837\pi$
$349$			324.359i			0.929396i	−0.885469	+	0.464698i	$0.846163\pi$
$350$		0			0
$351$	−55.6388			−0.158515
$352$		0			0
$353$	−573.272	+	90.7973i	−1.62400	+	0.257216i	−0.901060	−	0.433695i	$-0.857210\pi$
$353$	−573.272	+	90.7973i	−1.62400	+	0.257216i	−0.722940	+	0.690911i	$0.757210\pi$
$354$		0			0
$355$	−98.8576	+	56.4017i	−0.278472	+	0.158878i
$356$		0			0
$357$	187.937	+	187.937i	0.526434	+	0.526434i
$358$		0			0
$359$	−348.589	+	113.264i	−0.971001	+	0.315497i	−0.751220	−	0.660052i	$-0.770534\pi$
$359$	−348.589	+	113.264i	−0.971001	+	0.315497i	−0.219781	+	0.975549i	$0.570534\pi$
$360$		0			0
$361$	−86.5680	+	266.429i	−0.239801	+	0.738030i
$362$		0			0
$363$	−424.210	−	216.146i	−1.16862	−	0.595443i
$364$		0			0
$365$	−52.7457	+	2.49322i	−0.144509	+	0.00683074i
$366$		0			0
$367$	410.639	+	65.0389i	1.11891	+	0.177218i	0.688373	−	0.725357i	$-0.258325\pi$
$367$	410.639	+	65.0389i	1.11891	+	0.177218i	0.430534	+	0.902574i	$0.358325\pi$
$368$		0			0
$369$	73.3997	+	101.026i	0.198915	+	0.273783i
$370$		0			0
$371$	293.924	+	213.548i	0.792247	+	0.575601i
$372$		0			0
$373$	1.77772	+	3.48897i	0.00476600	+	0.00935381i	0.893377	−	0.449307i	$-0.148329\pi$
$373$	1.77772	+	3.48897i	0.00476600	+	0.00935381i	−0.888611	+	0.458661i	$0.848329\pi$
$374$		0			0
$375$	441.902	−	216.666i	1.17841	−	0.577775i
$376$		0			0
$377$	224.237	−	114.255i	0.594794	−	0.303063i
$378$		0			0
$379$	155.189	−	213.599i	0.409470	−	0.563586i	−0.553619	−	0.832770i	$-0.686754\pi$
$379$	155.189	−	213.599i	0.409470	−	0.563586i	0.963089	+	0.269183i	$0.0867538\pi$
$380$		0			0
$381$	389.188	−	282.761i	1.02149	−	0.742156i
$382$		0			0
$383$	−78.4913	+	495.574i	−0.204938	+	1.29393i	0.643832	+	0.765167i	$0.277343\pi$
$383$	−78.4913	+	495.574i	−0.204938	+	1.29393i	−0.848770	+	0.528761i	$0.822657\pi$
$384$		0			0
$385$	0.477970	+	10.1118i	0.00124148	+	0.0262644i
$386$		0			0
$387$	−98.3845	+	193.091i	−0.254224	+	0.498942i
$388$		0			0
$389$	364.326	+	118.377i	0.936571	+	0.304310i	0.737247	−	0.675623i	$-0.236125\pi$
$389$	364.326	+	118.377i	0.936571	+	0.304310i	0.199324	+	0.979934i	$0.436125\pi$
$390$		0			0
$391$	−73.5837	−	226.467i	−0.188194	−	0.579201i
$392$		0			0
$393$	504.506	−	504.506i	1.28373	−	1.28373i
$394$		0			0
$395$	−301.331	−	528.155i	−0.762864	−	1.33710i
$396$		0			0
$397$	−51.3528	−	324.229i	−0.129352	−	0.816697i	−0.963998	−	0.265910i	$-0.914328\pi$
$397$	−51.3528	−	324.229i	−0.129352	−	0.816697i	0.834646	−	0.550787i	$-0.185672\pi$
$398$		0			0
$399$			720.888i			1.80674i
$400$		0			0
$401$	−54.4458			−0.135775			−0.0678875	−	0.997693i	$-0.521626\pi$
$401$	−54.4458			−0.135775			−0.0678875	+	0.997693i	$0.521626\pi$
$402$		0			0
$403$	305.827	−	48.4383i	0.758877	−	0.120194i
$404$		0			0
$405$	98.6487	+	476.094i	0.243577	+	1.17554i
$406$		0			0
$407$	7.71169	+	7.71169i	0.0189476	+	0.0189476i
$408$		0			0
$409$	149.018	−	48.4188i	0.364347	−	0.118383i	−0.121122	−	0.992638i	$-0.538649\pi$
$409$	149.018	−	48.4188i	0.364347	−	0.118383i	0.485468	+	0.874254i	$0.338649\pi$
$410$		0			0
$411$	−43.0756	+	132.573i	−0.104807	+	0.322562i
$412$		0			0
$413$	−495.719	−	252.581i	−1.20029	−	0.611577i
$414$		0			0
$415$	108.206	+	71.0610i	0.260737	+	0.171231i
$416$		0			0
$417$	224.799	+	35.6046i	0.539086	+	0.0853828i
$418$		0			0
$419$	−296.787	−	408.492i	−0.708321	−	0.974920i	−0.999832	−	0.0183527i	$-0.994158\pi$
$419$	−296.787	−	408.492i	−0.708321	−	0.974920i	0.291510	−	0.956568i	$-0.405842\pi$
$420$		0			0
$421$	−599.885	−	435.842i	−1.42491	−	1.03525i	−0.990937	−	0.134327i	$-0.957113\pi$
$421$	−599.885	−	435.842i	−1.42491	−	1.03525i	−0.433969	−	0.900928i	$-0.642887\pi$
$422$		0			0
$423$	55.5785	+	109.079i	0.131391	+	0.257870i
$424$		0			0
$425$	−125.098	−	197.027i	−0.294348	−	0.463594i
$426$		0			0
$427$	670.403	−	341.587i	1.57003	−	0.799970i
$428$		0			0
$429$	3.66590	−	5.04567i	0.00854521	−	0.0117615i
$430$		0			0
$431$	588.734	−	427.740i	1.36597	−	0.992437i	0.367933	−	0.929852i	$-0.380066\pi$
$431$	588.734	−	427.740i	1.36597	−	0.992437i	0.998040	−	0.0625850i	$-0.0199345\pi$
$432$		0			0
$433$	−34.7237	+	219.237i	−0.0801932	+	0.506320i	0.914596	+	0.404369i	$0.132509\pi$
$433$	−34.7237	+	219.237i	−0.0801932	+	0.506320i	−0.994789	+	0.101952i	$0.967491\pi$
$434$		0			0
$435$	−547.624	−	683.393i	−1.25891	−	1.57102i
$436$		0			0
$437$	293.216	−	575.468i	0.670974	−	1.31686i
$438$		0			0
$439$	245.012	+	79.6092i	0.558113	+	0.181342i	0.574472	−	0.818524i	$-0.305207\pi$
$439$	245.012	+	79.6092i	0.558113	+	0.181342i	−0.0163587	+	0.999866i	$0.505207\pi$
$440$		0			0
$441$	6.60374	+	20.3242i	0.0149745	+	0.0460867i
$442$		0			0
$443$	60.0305	−	60.0305i	0.135509	−	0.135509i	−0.636099	−	0.771608i	$-0.719453\pi$
$443$	60.0305	−	60.0305i	0.135509	−	0.135509i	0.771608	+	0.636099i	$0.219453\pi$
$444$		0			0
$445$	−69.2405	+	76.1111i	−0.155597	+	0.171036i
$446$		0			0
$447$	−148.976	−	940.596i	−0.333279	−	2.10424i
$448$		0			0
$449$		−	142.467i		−	0.317299i	−0.987335	−	0.158649i	$-0.949286\pi$
$449$		−	142.467i		−	0.317299i	0.987335	−	0.158649i	$-0.0507139\pi$
$450$		0			0
$451$	5.37730			0.0119231
$452$		0			0
$453$	367.490	−	58.2046i	0.811235	−	0.128487i
$454$		0			0
$455$	203.310	+	22.4230i	0.446835	+	0.0492814i
$456$		0			0
$457$	265.053	+	265.053i	0.579986	+	0.579986i	0.934899	−	0.354914i	$-0.115490\pi$
$457$	265.053	+	265.053i	0.579986	+	0.579986i	−0.354914	+	0.934899i	$0.615490\pi$
$458$		0			0
$459$	87.3175	−	28.3712i	0.190234	−	0.0618108i
$460$		0			0
$461$	−221.105	+	680.490i	−0.479620	+	1.47612i	0.360005	+	0.932950i	$0.382775\pi$
$461$	−221.105	+	680.490i	−0.479620	+	1.47612i	−0.839624	+	0.543167i	$0.817225\pi$
$462$		0			0
$463$	−520.235	−	265.073i	−1.12362	−	0.572512i	−0.209439	−	0.977822i	$-0.567164\pi$
$463$	−520.235	−	265.073i	−1.12362	−	0.572512i	−0.914179	+	0.405310i	$0.867164\pi$
$464$		0			0
$465$	−380.968	−	1007.87i	−0.819287	−	2.16746i
$466$		0			0
$467$	826.139	+	130.848i	1.76903	+	0.280187i	0.954126	−	0.299404i	$-0.0967879\pi$
$467$	826.139	+	130.848i	1.76903	+	0.280187i	0.814907	+	0.579591i	$0.196788\pi$
$468$		0			0
$469$	−129.076	−	177.658i	−0.275216	−	0.378802i
$470$		0			0
$471$	843.995	+	613.198i	1.79192	+	1.30191i
$472$		0			0
$473$	4.23658	+	8.31476i	0.00895683	+	0.0175788i
$474$		0			0
$475$	137.953	−	617.804i	0.290428	−	1.30064i
$476$		0			0
$477$	−291.086	+	148.316i	−0.610243	+	0.310934i
$478$		0			0
$479$	229.058	−	315.271i	0.478201	−	0.658187i	−0.499957	−	0.866050i	$-0.666651\pi$
$479$	229.058	−	315.271i	0.478201	−	0.658187i	0.978158	+	0.207863i	$0.0666509\pi$
$480$		0			0
$481$	178.276	−	129.525i	0.370637	−	0.269283i
$482$		0			0
$483$	113.602	−	717.258i	0.235202	−	1.48501i
$484$		0			0
$485$	−722.484	−	197.564i	−1.48966	−	0.407349i
$486$		0			0
$487$	−81.6474	+	160.242i	−0.167654	+	0.329039i	−0.959513	−	0.281665i	$-0.909113\pi$
$487$	−81.6474	+	160.242i	−0.167654	+	0.329039i	0.791859	+	0.610704i	$0.209113\pi$
$488$		0			0
$489$	−167.029	−	54.2709i	−0.341572	−	0.110983i
$490$		0			0
$491$	−147.768	−	454.783i	−0.300953	−	0.926239i	−0.981156	−	0.193215i	$-0.938108\pi$
$491$	−147.768	−	454.783i	−0.300953	−	0.926239i	0.680203	−	0.733024i	$-0.261892\pi$
$492$		0			0
$493$	−293.649	+	293.649i	−0.595638	+	0.595638i
$494$		0			0
$495$	−8.29673	−	3.74502i	−0.0167611	−	0.00756571i
$496$		0			0
$497$	25.7489	+	162.572i	0.0518087	+	0.327107i
$498$		0			0
$499$		−	112.565i		−	0.225581i	−0.993619	−	0.112791i	$-0.964021\pi$
$499$		−	112.565i		−	0.225581i	0.993619	−	0.112791i	$-0.0359789\pi$
$500$		0			0
$501$	936.082			1.86843
$502$		0			0
$503$	211.275	−	33.4627i	0.420031	−	0.0665263i	0.0571582	−	0.998365i	$-0.481796\pi$
$503$	211.275	−	33.4627i	0.420031	−	0.0665263i	0.362872	+	0.931839i	$0.381796\pi$
$504$		0			0
$505$	−99.5880	+	220.628i	−0.197204	+	0.436886i
$506$		0			0
$507$	381.401	+	381.401i	0.752270	+	0.752270i
$508$		0			0
$509$	295.169	−	95.9061i	0.579899	−	0.188421i	−0.00435637	−	0.999991i	$-0.501387\pi$
$509$	295.169	−	95.9061i	0.579899	−	0.188421i	0.584255	+	0.811570i	$0.301387\pi$
$510$		0			0
$511$	−23.5982	+	72.6278i	−0.0461805	+	0.142129i
$512$		0			0
$513$	221.879	+	113.053i	0.432513	+	0.220376i
$514$		0			0
$515$	−160.289	+	586.172i	−0.311241	+	1.13820i
$516$		0			0
$517$	5.20677	+	0.824671i	0.0100711	+	0.00159511i
$518$		0			0
$519$	646.519	+	889.858i	1.24570	+	1.71456i
$520$		0			0
$521$	399.823	+	290.488i	0.767414	+	0.557559i	0.901175	−	0.433455i	$-0.142706\pi$
$521$	399.823	+	290.488i	0.767414	+	0.557559i	−0.133761	+	0.991014i	$0.542706\pi$
$522$		0			0
$523$	−34.6555	−	68.0152i	−0.0662628	−	0.130048i	0.855499	−	0.517804i	$-0.173250\pi$
$523$	−34.6555	−	68.0152i	−0.0662628	−	0.130048i	−0.921762	+	0.387756i	$0.873250\pi$
$524$		0			0
$525$	−67.1376	−	708.583i	−0.127881	−	1.34968i
$526$		0			0
$527$	−455.255	+	231.964i	−0.863861	+	0.440159i
$528$		0			0
$529$	−71.4868	+	98.3931i	−0.135136	+	0.185998i
$530$		0			0
$531$	404.739	−	294.060i	0.762221	−	0.553786i
$532$		0			0
$533$	16.9968	−	107.314i	0.0318890	−	0.201339i
$534$		0			0
$535$	693.401	−	262.101i	1.29608	−	0.489909i
$536$		0			0
$537$	−166.379	+	326.537i	−0.309830	+	0.608076i
$538$		0			0
$539$	0.875191	+	0.284367i	0.00162373	+	0.000527582i
$540$		0			0
$541$	−111.558	−	343.339i	−0.206207	−	0.634639i	−0.999662	−	0.0260098i	$-0.991720\pi$
$541$	−111.558	−	343.339i	−0.206207	−	0.634639i	0.793455	−	0.608629i	$-0.208280\pi$
$542$		0			0
$543$	−970.556	+	970.556i	−1.78740	+	1.78740i
$544$		0			0
$545$	78.8913	−	715.308i	0.144755	−	1.31249i
$546$		0			0
$547$	−80.2610	−	506.748i	−0.146729	−	0.926413i	−0.945699	−	0.325042i	$-0.894621\pi$
$547$	−80.2610	−	506.748i	−0.146729	−	0.926413i	0.798970	−	0.601371i	$-0.205379\pi$
$548$		0			0
$549$			676.578i			1.23238i
$550$		0			0
$551$	−1126.38			−2.04425
$552$		0			0
$553$	−868.557	+	137.566i	−1.57063	+	0.248763i
$554$		0			0
$555$	−567.208	−	516.006i	−1.02200	−	0.929741i
$556$		0			0
$557$	633.877	+	633.877i	1.13802	+	1.13802i	0.988805	+	0.149215i	$0.0476747\pi$
$557$	633.877	+	633.877i	1.13802	+	1.13802i	0.149215	+	0.988805i	$0.452325\pi$
$558$		0			0
$559$	179.327	−	58.2670i	0.320800	−	0.104234i
$560$		0			0
$561$	−3.18025	+	9.78780i	−0.00566889	+	0.0174471i
$562$		0			0
$563$	554.252	+	282.405i	0.984462	+	0.501608i	0.870655	−	0.491895i	$-0.163695\pi$
$563$	554.252	+	282.405i	0.984462	+	0.501608i	0.113807	+	0.993503i	$0.463695\pi$
$564$		0			0
$565$	534.819	−	428.567i	0.946582	−	0.758526i
$566$		0			0
$567$	694.490	+	109.996i	1.22485	+	0.193997i
$568$		0			0
$569$	448.044	+	616.680i	0.787423	+	1.08380i	0.994424	+	0.105455i	$0.0336297\pi$
$569$	448.044	+	616.680i	0.787423	+	1.08380i	−0.207001	+	0.978341i	$0.566370\pi$
$570$		0			0
$571$	−104.927	−	76.2337i	−0.183760	−	0.133509i	0.492103	−	0.870537i	$-0.336229\pi$
$571$	−104.927	−	76.2337i	−0.183760	−	0.133509i	−0.675862	+	0.737028i	$0.736229\pi$
$572$		0			0
$573$	170.835	+	335.282i	0.298141	+	0.585135i
$574$		0			0
$575$	−234.616	+	592.953i	−0.408028	+	1.03122i
$576$		0			0
$577$	−667.653	+	340.186i	−1.15711	+	0.589578i	−0.923819	−	0.382829i	$-0.874950\pi$
$577$	−667.653	+	340.186i	−1.15711	+	0.589578i	−0.233292	+	0.972407i	$0.574950\pi$
$578$		0			0
$579$	148.032	−	203.749i	0.255669	−	0.351898i
$580$		0			0
$581$	151.459	−	110.042i	0.260688	−	0.189401i
$582$		0			0
$583$	−2.20070	+	13.8947i	−0.00377479	+	0.0238331i
$584$		0			0
$585$	−100.964	+	153.739i	−0.172587	+	0.262802i
$586$		0			0
$587$	−207.881	+	407.988i	−0.354141	+	0.695040i	−0.997511	−	0.0705153i	$-0.977536\pi$
$587$	−207.881	+	407.988i	−0.354141	+	0.695040i	0.643370	+	0.765555i	$0.277536\pi$
$588$		0			0
$589$	−1318.02	−	428.250i	−2.23772	−	0.727079i
$590$		0			0
$591$	−158.212	−	486.926i	−0.267702	−	0.823902i
$592$		0			0
$593$	−142.290	+	142.290i	−0.239950	+	0.239950i	−0.816829	−	0.576879i	$-0.804270\pi$
$593$	−142.290	+	142.290i	−0.239950	+	0.239950i	0.576879	+	0.816829i	$0.304270\pi$
$594$		0			0
$595$	−330.501	+	68.4812i	−0.555464	+	0.115094i
$596$		0			0
$597$	−102.170	−	645.075i	−0.171139	−	1.08053i
$598$		0			0
$599$			123.484i			0.206150i	0.994674	+	0.103075i	$0.0328682\pi$
$599$			123.484i			0.206150i	−0.994674	+	0.103075i	$0.967132\pi$
$600$		0			0
$601$	512.898			0.853407			0.426704	−	0.904392i	$-0.359675\pi$
$601$	512.898			0.853407			0.426704	+	0.904392i	$0.359675\pi$
$602$		0			0
$603$	195.034	−	30.8903i	0.323439	−	0.0512278i
$604$		0			0
$605$	525.149	−	299.616i	0.868014	−	0.495233i
$606$		0			0
$607$	−164.317	−	164.317i	−0.270703	−	0.270703i	0.558680	−	0.829383i	$-0.311308\pi$
$607$	−164.317	−	164.317i	−0.270703	−	0.270703i	−0.829383	+	0.558680i	$0.811308\pi$
$608$		0			0
$609$	−1204.50	+	391.365i	−1.97783	+	0.642636i
$610$		0			0
$611$	32.9156	−	101.304i	0.0538717	−	0.165800i
$612$		0			0
$613$	794.593	+	404.865i	1.29624	+	0.660465i	0.959653	−	0.281189i	$-0.0907286\pi$
$613$	794.593	+	404.865i	1.29624	+	0.660465i	0.336583	+	0.941654i	$0.390729\pi$
$614$		0			0
$615$	−377.658	+	17.8514i	−0.614079	+	0.0290267i
$616$		0			0
$617$	430.183	+	68.1342i	0.697217	+	0.110428i	0.494975	−	0.868907i	$-0.335177\pi$
$617$	430.183	+	68.1342i	0.697217	+	0.110428i	0.202242	+	0.979336i	$0.435177\pi$
$618$		0			0
$619$	−446.704	−	614.835i	−0.721654	−	0.993271i	−0.999467	−	0.0326364i	$-0.989610\pi$
$619$	−446.704	−	614.835i	−0.721654	−	0.993271i	0.277813	−	0.960635i	$-0.410390\pi$
$620$		0			0
$621$	−202.946	−	147.449i	−0.326805	−	0.237438i
$622$		0			0
$623$	67.5557	+	132.585i	0.108436	+	0.212818i
$624$		0			0
$625$	−78.0613	+	620.106i	−0.124898	+	0.992170i
$626$		0			0
$627$	−24.8714	+	12.6726i	−0.0396673	+	0.0202115i
$628$		0			0
$629$	−213.733	+	294.178i	−0.339798	+	0.467692i
$630$		0			0
$631$	496.536	−	360.754i	0.786903	−	0.571719i	−0.120140	−	0.992757i	$-0.538334\pi$
$631$	496.536	−	360.754i	0.786903	−	0.571719i	0.907043	+	0.421038i	$0.138334\pi$
$632$		0			0
$633$	−69.7072	+	440.114i	−0.110122	+	0.695283i
$634$		0			0
$635$	28.8446	+	610.226i	0.0454245	+	0.960985i
$636$		0			0
$637$	8.44140	−	16.5672i	0.0132518	−	0.0260081i
$638$		0			0
$639$	−140.765	−	45.7375i	−0.220290	−	0.0715767i
$640$		0			0
$641$	8.01015	+	24.6527i	0.0124963	+	0.0384598i	0.957110	−	0.289724i	$-0.0935635\pi$
$641$	8.01015	+	24.6527i	0.0124963	+	0.0384598i	−0.944614	+	0.328184i	$0.893563\pi$
$642$		0			0
$643$	−307.458	+	307.458i	−0.478162	+	0.478162i	−0.904543	−	0.426381i	$-0.859788\pi$
$643$	−307.458	+	307.458i	−0.478162	+	0.478162i	0.426381	+	0.904543i	$0.359788\pi$
$644$		0			0
$645$	−325.146	−	569.897i	−0.504103	−	0.883561i
$646$		0			0
$647$	25.5238	+	161.151i	0.0394494	+	0.249074i	0.999530	−	0.0306491i	$-0.00975744\pi$
$647$	25.5238	+	161.151i	0.0394494	+	0.249074i	−0.960081	+	0.279723i	$0.909757\pi$
$648$		0			0
$649$		−	21.5430i		−	0.0331941i
$650$		0			0
$651$	−1558.22			−2.39358
$652$		0			0
$653$	−181.554	+	28.7553i	−0.278030	+	0.0440357i	−0.293892	−	0.955838i	$-0.594951\pi$
$653$	−181.554	+	28.7553i	−0.278030	+	0.0440357i	0.0158620	+	0.999874i	$0.494951\pi$
$654$		0			0
$655$	183.834	+	887.211i	0.280663	+	1.35452i
$656$		0			0
$657$	−48.5562	−	48.5562i	−0.0739060	−	0.0739060i
$658$		0			0
$659$	−308.361	+	100.193i	−0.467923	+	0.152038i	−0.533482	−	0.845811i	$-0.679117\pi$
$659$	−308.361	+	100.193i	−0.467923	+	0.152038i	0.0655590	+	0.997849i	$0.479117\pi$
$660$		0			0
$661$	−121.643	+	374.378i	−0.184028	+	0.566381i	−0.999930	−	0.0118092i	$-0.996241\pi$
$661$	−121.643	+	374.378i	−0.184028	+	0.566381i	0.815902	+	0.578190i	$0.196241\pi$
$662$		0			0
$663$	185.281	+	94.4054i	0.279459	+	0.142391i
$664$		0			0
$665$	−765.207	−	502.527i	−1.15069	−	0.755680i
$666$		0			0
$667$	1120.71	+	177.503i	1.68022	+	0.266121i
$668$		0			0
$669$	−391.939	−	539.457i	−0.585857	−	0.806364i
$670$		0			0
$671$	23.5702	+	17.1248i	0.0351270	+	0.0255213i
$672$		0			0
$673$	−208.434	−	409.074i	−0.309708	−	0.607837i	0.682718	−	0.730682i	$-0.260798\pi$
$673$	−208.434	−	409.074i	−0.309708	−	0.607837i	−0.992426	+	0.122846i	$0.960798\pi$
$674$		0			0
$675$	−228.621	−	90.4594i	−0.338697	−	0.134014i
$676$		0			0
$677$	−49.8554	+	25.4026i	−0.0736417	+	0.0375223i	−0.490424	−	0.871484i	$-0.663158\pi$
$677$	−49.8554	+	25.4026i	−0.0736417	+	0.0375223i	0.416782	+	0.909007i	$0.363158\pi$
$678$		0			0
$679$	−636.694	+	876.335i	−0.937694	+	1.29063i
$680$		0			0
$681$	1265.97	−	919.784i	1.85899	−	1.35064i
$682$		0			0
$683$	−0.429989	+	2.71484i	−0.000629559	+	0.00397488i	−0.988001	−	0.154447i	$-0.950641\pi$
$683$	−0.429989	+	2.71484i	−0.000629559	+	0.00397488i	0.987372	+	0.158422i	$0.0506405\pi$
$684$		0			0
$685$	−110.696	−	138.140i	−0.161599	−	0.201664i
$686$		0			0
$687$	−328.670	+	645.051i	−0.478413	+	0.938939i
$688$		0			0
$689$	270.338	+	87.8380i	0.392362	+	0.127486i
$690$		0			0
$691$	−41.5358	−	127.834i	−0.0601097	−	0.184999i	0.916493	−	0.400051i	$-0.131008\pi$
$691$	−41.5358	−	127.834i	−0.0601097	−	0.184999i	−0.976602	+	0.215053i	$0.931008\pi$
$692$		0			0
$693$	−9.30862	+	9.30862i	−0.0134324	+	0.0134324i
$694$		0			0
$695$	−194.500	+	213.799i	−0.279855	+	0.307625i
$696$		0			0
$697$	28.0469	+	177.081i	0.0402395	+	0.254062i
$698$		0			0
$699$		−	1155.56i		−	1.65316i
$700$		0			0
$701$	−264.123			−0.376780			−0.188390	−	0.982094i	$-0.560327\pi$
$701$	−264.123			−0.376780			−0.188390	+	0.982094i	$0.560327\pi$
$702$		0			0
$703$	−974.124	+	154.286i	−1.38567	+	0.219468i
$704$		0			0
$705$	−368.419	−	40.6330i	−0.522580	−	0.0576354i
$706$		0			0
$707$	247.536	+	247.536i	0.350121	+	0.350121i
$708$		0			0
$709$	−854.165	+	277.535i	−1.20475	+	0.391446i	−0.841505	−	0.540249i	$-0.818330\pi$
$709$	−854.165	+	277.535i	−1.20475	+	0.391446i	−0.363242	+	0.931695i	$0.618330\pi$
$710$		0			0
$711$	244.357	−	752.052i	0.343680	−	1.05774i
$712$		0			0
$713$	1243.89	+	633.795i	1.74459	+	0.888913i
$714$		0			0
$715$	2.80040	+	7.40858i	0.00391664	+	0.0103617i
$716$		0			0
$717$	73.0902	+	11.5763i	0.101939	+	0.0161455i
$718$		0			0
$719$	−719.629	−	990.484i	−1.00087	−	1.37759i	−0.924787	−	0.380485i	$-0.875757\pi$
$719$	−719.629	−	990.484i	−1.00087	−	1.37759i	−0.0760877	−	0.997101i	$-0.524243\pi$
$720$		0			0
$721$	710.995	+	516.568i	0.986124	+	0.716461i
$722$		0			0
$723$	621.729	+	1220.21i	0.859930	+	1.68771i
$724$		0			0
$725$	1107.15	−	104.902i	1.52711	−	0.144692i
$726$		0			0
$727$	597.726	−	304.557i	0.822182	−	0.418923i	0.00830916	−	0.999965i	$-0.497355\pi$
$727$	597.726	−	304.557i	0.822182	−	0.418923i	0.813873	+	0.581043i	$0.197355\pi$
$728$		0			0
$729$	−166.804	+	229.586i	−0.228812	+	0.314932i
$730$		0			0
$731$	−251.718	+	182.884i	−0.344348	+	0.250184i
$732$		0			0
$733$	23.5240	−	148.525i	0.0320928	−	0.202626i	−0.966432	−	0.256922i	$-0.917292\pi$
$733$	23.5240	−	148.525i	0.0320928	−	0.202626i	0.998525	+	0.0542964i	$0.0172916\pi$
$734$		0			0
$735$	−62.4104	−	17.0662i	−0.0849121	−	0.0232193i
$736$		0			0
$737$	3.86034	−	7.57635i	0.00523791	−	0.0102800i
$738$		0			0
$739$	−62.7595	−	20.3918i	−0.0849249	−	0.0275938i	0.266246	−	0.963905i	$-0.414217\pi$
$739$	−62.7595	−	20.3918i	−0.0849249	−	0.0275938i	−0.351171	+	0.936311i	$0.614217\pi$
$740$		0			0
$741$	174.290	+	536.411i	0.235210	+	0.723901i
$742$		0			0
$743$	−425.112	+	425.112i	−0.572156	+	0.572156i	−0.932730	−	0.360574i	$-0.882581\pi$
$743$	−425.112	+	425.112i	−0.572156	+	0.572156i	0.360574	+	0.932730i	$0.382581\pi$
$744$		0			0
$745$	1102.27	+	497.550i	1.47956	+	0.667852i
$746$		0			0
$747$	26.3351	+	166.273i	0.0352544	+	0.222588i
$748$		0			0
$749$		−	1072.04i		−	1.43129i
$750$		0			0
$751$	903.975			1.20370			0.601848	−	0.798611i	$-0.294431\pi$
$751$	903.975			1.20370			0.601848	+	0.798611i	$0.294431\pi$
$752$		0			0
$753$	1393.33	−	220.681i	1.85037	−	0.293069i
$754$		0			0
$755$	−194.392	+	430.656i	−0.257473	+	0.570406i
$756$		0			0
$757$	334.979	+	334.979i	0.442508	+	0.442508i	0.892854	−	0.450346i	$-0.148699\pi$
$757$	334.979	+	334.979i	0.442508	+	0.442508i	−0.450346	+	0.892854i	$0.648699\pi$
$758$		0			0
$759$	26.7432	−	8.68939i	0.0352348	−	0.0114485i
$760$		0			0
$761$	43.3702	−	133.480i	0.0569911	−	0.175401i	−0.918509	−	0.395401i	$-0.870606\pi$
$761$	43.3702	−	133.480i	0.0569911	−	0.175401i	0.975500	+	0.220000i	$0.0706058\pi$
$762$		0			0
$763$	−927.309	−	472.488i	−1.21535	−	0.619250i
$764$		0			0
$765$	80.0543	−	292.755i	0.104646	−	0.382687i
$766$		0			0
$767$	−429.930	−	68.0942i	−0.560534	−	0.0887799i
$768$		0			0
$769$	52.0992	+	71.7085i	0.0677493	+	0.0932490i	0.841547	−	0.540184i	$-0.181645\pi$
$769$	52.0992	+	71.7085i	0.0677493	+	0.0932490i	−0.773798	+	0.633433i	$0.781645\pi$
$770$		0			0
$771$	423.063	+	307.373i	0.548719	+	0.398668i
$772$		0			0
$773$	431.889	+	847.630i	0.558718	+	1.09655i	0.981705	+	0.190410i	$0.0609818\pi$
$773$	431.889	+	847.630i	0.558718	+	1.09655i	−0.422986	+	0.906136i	$0.639018\pi$
$774$		0			0
$775$	1335.40	+	298.190i	1.72310	+	0.384762i
$776$		0			0
$777$	−988.075	+	503.450i	−1.27165	+	0.647940i
$778$		0			0
$779$	−285.833	+	393.416i	−0.366923	+	0.505026i
$780$		0			0
$781$	−5.15628	+	3.74625i	−0.00660215	+	0.00479674i
$782$		0			0
$783$	−68.4385	+	432.103i	−0.0874055	+	0.551856i
$784$		0			0
$785$	−1239.24	+	468.425i	−1.57865	+	0.596720i
$786$		0			0
$787$	−146.845	+	288.200i	−0.186589	+	0.366201i	−0.965284	−	0.261201i	$-0.915881\pi$
$787$	−146.845	+	288.200i	−0.186589	+	0.366201i	0.778696	+	0.627401i	$0.215881\pi$
$788$		0			0
$789$	136.033	+	44.1997i	0.172411	+	0.0560198i
$790$		0			0
$791$	−306.280	−	942.632i	−0.387206	−	1.19170i
$792$		0			0
$793$	416.258	−	416.258i	0.524916	−	0.524916i
$794$		0			0
$795$	108.432	−	983.156i	0.136393	−	1.23667i
$796$		0			0
$797$	−132.525	−	836.730i	−0.166280	−	1.04985i	−0.919789	−	0.392412i	$-0.871641\pi$
$797$	−132.525	−	836.730i	−0.166280	−	1.04985i	0.753510	−	0.657437i	$-0.228359\pi$
$798$		0			0
$799$			175.767i			0.219984i
$800$		0			0
$801$	−133.807			−0.167050
$802$		0			0
$803$	−2.92057	+	0.462574i	−0.00363708	+	0.000576057i
$804$		0			0
$805$	682.162	+	620.583i	0.847406	+	0.770911i
$806$		0			0
$807$	599.468	+	599.468i	0.742835	+	0.742835i
$808$		0			0
$809$	−209.176	+	67.9655i	−0.258561	+	0.0840117i	−0.435429	−	0.900223i	$-0.643403\pi$
$809$	−209.176	+	67.9655i	−0.258561	+	0.0840117i	0.176868	+	0.984235i	$0.443403\pi$
$810$		0			0
$811$	77.6057	−	238.846i	0.0956913	−	0.294508i	−0.891742	−	0.452544i	$-0.850516\pi$
$811$	77.6057	−	238.846i	0.0956913	−	0.294508i	0.987433	+	0.158037i	$0.0505164\pi$
$812$		0			0
$813$	−660.180	−	336.378i	−0.812029	−	0.413750i
$814$		0			0
$815$	174.042	−	139.465i	0.213549	−	0.171123i
$816$		0			0
$817$	−833.524	−	132.017i	−1.02023	−	0.161588i
$818$		0			0
$819$	156.347	+	215.194i	0.190900	+	0.262752i
$820$		0			0
$821$	−1005.92	−	730.846i	−1.22524	−	0.890190i	−0.228717	−	0.973493i	$-0.573453\pi$
$821$	−1005.92	−	730.846i	−1.22524	−	0.890190i	−0.996524	+	0.0833033i	$0.973453\pi$
$822$		0			0
$823$	−58.3047	−	114.429i	−0.0708442	−	0.139039i	0.852868	−	0.522126i	$-0.174861\pi$
$823$	−58.3047	−	114.429i	−0.0708442	−	0.139039i	−0.923712	+	0.383087i	$0.874861\pi$
$824$		0			0
$825$	23.2666	−	14.7726i	0.0282020	−	0.0179062i
$826$		0			0
$827$	−611.364	+	311.506i	−0.739255	+	0.376669i	−0.782710	−	0.622386i	$-0.786163\pi$
$827$	−611.364	+	311.506i	−0.739255	+	0.376669i	0.0434552	+	0.999055i	$0.486163\pi$
$828$		0			0
$829$	−722.996	+	995.118i	−0.872130	+	1.20038i	0.106409	+	0.994322i	$0.466065\pi$
$829$	−722.996	+	995.118i	−0.872130	+	1.20038i	−0.978539	+	0.206061i	$0.933935\pi$
$830$		0			0
$831$	648.738	−	471.336i	0.780672	−	0.567191i
$832$		0			0
$833$	−4.79974	+	30.3044i	−0.00576199	+	0.0363798i
$834$		0			0
$835$	−652.537	+	993.631i	−0.781482	+	1.18998i
$836$		0			0
$837$	−244.368	+	479.599i	−0.291957	+	0.572998i
$838$		0			0
$839$	−358.353	−	116.436i	−0.427120	−	0.138780i	0.0875656	−	0.996159i	$-0.472091\pi$
$839$	−358.353	−	116.436i	−0.427120	−	0.138780i	−0.514685	+	0.857379i	$0.672091\pi$
$840$		0			0
$841$	−351.621	−	1082.18i	−0.418099	−	1.28678i
$842$		0			0
$843$	893.271	−	893.271i	1.05963	−	1.05963i
$844$		0			0
$845$	−670.721	+	138.976i	−0.793753	+	0.164469i
$846$		0			0
$847$	−136.783	−	863.613i	−0.161491	−	1.01961i
$848$		0			0
$849$			412.710i			0.486113i
$850$		0			0
$851$	993.531			1.16749
$852$		0			0
$853$	30.6258	−	4.85064i	0.0359036	−	0.00568657i	−0.138457	−	0.990368i	$-0.544214\pi$
$853$	30.6258	−	4.85064i	0.0359036	−	0.00568657i	0.174360	+	0.984682i	$0.444214\pi$
$854$		0			0
$855$	715.012	−	407.939i	0.836271	−	0.477122i
$856$		0			0
$857$	−530.847	−	530.847i	−0.619424	−	0.619424i	0.325959	−	0.945384i	$-0.394313\pi$
$857$	−530.847	−	530.847i	−0.619424	−	0.619424i	−0.945384	+	0.325959i	$0.894313\pi$
$858$		0			0
$859$	−1220.02	+	396.408i	−1.42028	+	0.461476i	−0.915691	−	0.401884i	$-0.868355\pi$
$859$	−1220.02	+	396.408i	−1.42028	+	0.461476i	−0.504588	+	0.863360i	$0.668355\pi$
$860$		0			0
$861$	−168.963	+	520.014i	−0.196240	+	0.603966i
$862$		0			0
$863$	583.573	+	297.345i	0.676214	+	0.344548i	0.758142	−	0.652090i	$-0.226108\pi$
$863$	583.573	+	297.345i	0.676214	+	0.344548i	−0.0819275	+	0.996638i	$0.526108\pi$
$864$		0			0
$865$	−1395.25	+	65.9516i	−1.61301	+	0.0762447i
$866$		0			0
$867$	784.952	+	124.324i	0.905366	+	0.143396i
$868$		0			0
$869$	−20.0147	−	27.5479i	−0.0230319	−	0.0317006i
$870$		0			0
$871$	−138.998	−	100.988i	−0.159584	−	0.115945i
$872$		0			0
$873$	−442.203	−	867.873i	−0.506533	−	0.994127i
$874$		0			0
$875$	798.947	+	422.684i	0.913082	+	0.483068i
$876$		0			0
$877$	−99.6739	+	50.7864i	−0.113653	+	0.0579092i	−0.509893	−	0.860238i	$-0.670315\pi$
$877$	−99.6739	+	50.7864i	−0.113653	+	0.0579092i	0.396240	+	0.918147i	$0.370315\pi$
$878$		0			0
$879$	199.199	−	274.174i	0.226620	−	0.311916i
$880$		0			0
$881$	−1204.60	+	875.195i	−1.36731	+	0.993411i	−0.369371	+	0.929282i	$0.620427\pi$
$881$	−1204.60	+	875.195i	−1.36731	+	0.993411i	−0.997942	+	0.0641289i	$0.979573\pi$
$882$		0			0
$883$	−162.958	+	1028.88i	−0.184551	+	1.16521i	0.705284	+	0.708925i	$0.250820\pi$
$883$	−162.958	+	1028.88i	−0.184551	+	1.16521i	−0.889834	+	0.456283i	$0.849180\pi$
$884$		0			0
$885$	71.5178	+	1513.01i	0.0808111	+	1.70961i
$886$		0			0
$887$	83.4425	−	163.765i	0.0940727	−	0.184628i	−0.839175	−	0.543861i	$-0.816962\pi$
$887$	83.4425	−	163.765i	0.0940727	−	0.184628i	0.933248	+	0.359233i	$0.116962\pi$
$888$		0			0
$889$	840.247	+	273.013i	0.945159	+	0.307101i
$890$		0			0
$891$	8.41357	+	25.8943i	0.00944283	+	0.0290621i
$892$		0			0
$893$	−337.103	+	337.103i	−0.377495	+	0.377495i
$894$		0			0
$895$	−230.630	−	404.234i	−0.257687	−	0.451659i
$896$		0			0
$897$	−88.8814	−	561.175i	−0.0990874	−	0.625613i
$898$		0			0
$899$		−	2434.71i		−	2.70824i
$900$		0			0
$901$	−469.048			−0.520586
$902$		0			0
$903$	−937.202	+	148.438i	−1.03788	+	0.164383i
$904$		0			0
$905$	−353.655	−	1706.79i	−0.390779	−	1.88596i
$906$		0			0
$907$	1195.59	+	1195.59i	1.31818	+	1.31818i	0.915218	+	0.402959i	$0.132018\pi$
$907$	1195.59	+	1195.59i	1.31818	+	1.31818i	0.402959	+	0.915218i	$0.367982\pi$
$908$		0			0
$909$	−299.380	+	97.2743i	−0.329350	+	0.107012i
$910$		0			0
$911$	461.192	−	1419.40i	0.506248	−	1.55807i	−0.292414	−	0.956292i	$-0.594458\pi$
$911$	461.192	−	1419.40i	0.506248	−	1.55807i	0.798662	−	0.601780i	$-0.205542\pi$
$912$		0			0
$913$	6.45909	+	3.29107i	0.00707458	+	0.00360468i
$914$		0			0
$915$	−1712.23	−	1124.46i	−1.87129	−	1.22892i
$916$		0			0
$917$	1294.20	+	204.981i	1.41134	+	0.223534i
$918$		0			0
$919$	812.353	+	1118.11i	0.883953	+	1.21666i	0.975310	+	0.220838i	$0.0708793\pi$
$919$	812.353	+	1118.11i	0.883953	+	1.21666i	−0.0913577	+	0.995818i	$0.529121\pi$
$920$		0			0
$921$	1723.88	+	1252.47i	1.87175	+	1.35990i
$922$		0			0
$923$	58.4651	+	114.744i	0.0633425	+	0.124317i
$924$		0			0
$925$	943.127	−	242.374i	1.01960	−	0.262026i
$926$		0			0
$927$	−704.130	+	358.772i	−0.759579	+	0.387025i
$928$		0			0
$929$	−47.2332	+	65.0109i	−0.0508431	+	0.0699795i	−0.833682	−	0.552246i	$-0.813771\pi$
$929$	−47.2332	+	65.0109i	−0.0508431	+	0.0699795i	0.782838	+	0.622225i	$0.213771\pi$
$930$		0			0
$931$	−67.3261	+	48.9153i	−0.0723159	+	0.0525406i
$932$		0			0
$933$	−27.6789	+	174.758i	−0.0296665	+	0.187307i
$934$		0			0
$935$	−8.17260	−	10.1988i	−0.00874075	−	0.0109078i
$936$		0			0
$937$	−677.385	+	1329.44i	−0.722930	+	1.41883i	0.177630	+	0.984097i	$0.443157\pi$
$937$	−677.385	+	1329.44i	−0.722930	+	1.41883i	−0.900560	+	0.434732i	$0.856843\pi$
$938$		0			0
$939$	8.48898	+	2.75824i	0.00904045	+	0.00293742i
$940$		0			0
$941$	−156.957	−	483.065i	−0.166798	−	0.513353i	0.832366	−	0.554227i	$-0.186986\pi$
$941$	−156.957	−	483.065i	−0.166798	−	0.513353i	−0.999164	+	0.0408737i	$0.986986\pi$
$942$		0			0
$943$	346.391	−	346.391i	0.367329	−	0.367329i
$944$		0			0
$945$	−239.274	+	263.017i	−0.253200	+	0.278324i
$946$		0			0
$947$	4.90723	+	30.9831i	0.00518187	+	0.0327171i	0.990144	−	0.140054i	$-0.0447278\pi$
$947$	4.90723	+	30.9831i	0.00518187	+	0.0327171i	−0.984962	+	0.172772i	$0.944728\pi$
$948$		0			0
$949$			59.7475i			0.0629584i
$950$		0			0
$951$	−626.651			−0.658939
$952$		0			0
$953$	−907.936	+	143.803i	−0.952714	+	0.150895i	−0.613395	−	0.789776i	$-0.710197\pi$
$953$	−907.936	+	143.803i	−0.952714	+	0.150895i	−0.339319	+	0.940671i	$0.610197\pi$
$954$		0			0
$955$	−474.983	−	52.3859i	−0.497364	−	0.0548543i
$956$		0			0
$957$	−34.6766	−	34.6766i	−0.0362347	−	0.0362347i
$958$		0			0
$959$	−243.475	+	79.1098i	−0.253884	+	0.0824919i
$960$		0			0
$961$	628.710	−	1934.97i	0.654225	−	2.01350i
$962$		0			0
$963$	858.922	+	437.643i	0.891923	+	0.454458i
$964$		0			0
$965$	113.083	+	299.165i	0.117184	+	0.310016i
$966$		0			0
$967$	−714.279	−	113.131i	−0.738654	−	0.116991i	−0.224241	−	0.974534i	$-0.571990\pi$
$967$	−714.279	−	113.131i	−0.738654	−	0.116991i	−0.514413	+	0.857542i	$0.671990\pi$
$968$		0			0
$969$	−547.050	−	752.950i	−0.564551	−	0.777038i
$970$		0			0
$971$	1077.34	+	782.736i	1.10952	+	0.806113i	0.982588	−	0.185798i	$-0.0594870\pi$
$971$	1077.34	+	782.736i	1.10952	+	0.806113i	0.126932	+	0.991911i	$0.459487\pi$
$972$		0			0
$973$	189.767	+	372.438i	0.195033	+	0.382773i
$974$		0			0
$975$	−221.272	−	511.022i	−0.226946	−	0.524126i
$976$		0			0
$977$	812.379	−	413.928i	0.831503	−	0.423672i	0.0142134	−	0.999899i	$-0.495476\pi$
$977$	812.379	−	413.928i	0.831503	−	0.423672i	0.817290	+	0.576227i	$0.195476\pi$
$978$		0			0
$979$	−3.38677	+	4.66148i	−0.00345941	+	0.00476147i
$980$		0			0
$981$	757.119	−	550.079i	0.771783	−	0.560733i
$982$		0			0
$983$	166.604	−	1051.90i	0.169485	−	1.07009i	−0.745472	−	0.666537i	$-0.767776\pi$
$983$	166.604	−	1051.90i	0.169485	−	1.07009i	0.914957	−	0.403551i	$-0.132224\pi$
$984$		0			0
$985$	627.150	+	171.495i	0.636701	+	0.174107i
$986$		0			0
$987$	−243.355	+	477.611i	−0.246560	+	0.483901i
$988$		0			0
$989$	808.522	+	262.705i	0.817515	+	0.265627i
$990$		0			0
$991$	45.3053	+	139.435i	0.0457167	+	0.140702i	0.971309	−	0.237820i	$-0.0764327\pi$
$991$	45.3053	+	139.435i	0.0457167	+	0.140702i	−0.925593	+	0.378521i	$0.876433\pi$
$992$		0			0
$993$	867.011	−	867.011i	0.873123	−	0.873123i
$994$		0			0
$995$	755.955	+	341.227i	0.759754	+	0.342942i
$996$		0			0
$997$	−163.370	−	1031.48i	−0.163862	−	1.03458i	−0.923322	−	0.384028i	$-0.874537\pi$
$997$	−163.370	−	1031.48i	−0.163862	−	1.03458i	0.759460	−	0.650554i	$-0.225463\pi$
$998$		0			0
$999$			383.069i			0.383452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.f.97.2		64
4.3	odd	2		200.3.u.b.97.7	yes	64
25.8	odd	20	inner	400.3.bg.f.33.2		64
100.83	even	20		200.3.u.b.33.7	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.b.33.7	✓	64	100.83	even	20
200.3.u.b.97.7	yes	64	4.3	odd	2
400.3.bg.f.33.2		64	25.8	odd	20	inner
400.3.bg.f.97.2		64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.88880 + 0.615926i) q^{3} +(2.05707 - 4.55724i) q^{5} +(-5.11305 - 5.11305i) q^{7} +(6.18393 - 2.00928i) q^{9} +(0.0865225 - 0.266289i) q^{11} +(-5.04080 - 2.56841i) q^{13} +(-5.19263 + 18.9892i) q^{15} +(9.22052 + 1.46039i) q^{17} +(14.8832 + 20.4849i) q^{19} +(23.0329 + 16.7344i) q^{21} +(-11.5801 - 22.7271i) q^{23} +(-16.5369 - 18.7492i) q^{25} +(8.76274 - 4.46484i) q^{27} +(-26.1473 + 35.9887i) q^{29} +(-44.2788 + 32.1704i) q^{31} +(-0.172455 + 1.08884i) q^{33} +(-33.8193 + 12.7835i) q^{35} +(-17.6833 + 34.7055i) q^{37} +(21.1846 + 6.88330i) q^{39} +(5.93471 + 18.2652i) q^{41} +(-23.5671 + 23.5671i) q^{43} +(3.56401 - 32.3149i) q^{45} +(2.94533 + 18.5961i) q^{47} +3.28662i q^{49} -36.7563 q^{51} +(-49.6251 + 7.85985i) q^{53} +(-1.03556 - 0.942080i) q^{55} +(-70.4949 - 70.4949i) q^{57} +(73.1755 - 23.7762i) q^{59} +(-32.1545 + 98.9614i) q^{61} +(-41.8923 - 21.3452i) q^{63} +(-22.0742 + 17.6887i) q^{65} +(29.9952 + 4.75077i) q^{67} +(59.0308 + 81.2490i) q^{69} +(-18.4157 - 13.3798i) q^{71} +(-4.79456 - 9.40984i) q^{73} +(75.8569 + 62.7263i) q^{75} +(-1.80394 + 0.919155i) q^{77} +(71.4829 - 98.3877i) q^{79} +(-78.6699 + 57.1570i) q^{81} +(-4.05019 + 25.5719i) q^{83} +(25.6226 - 39.0160i) q^{85} +(79.5155 - 156.058i) q^{87} +(-19.5716 - 6.35919i) q^{89} +(12.6414 + 38.9063i) q^{91} +(152.377 - 152.377i) q^{93} +(123.970 - 25.6872i) q^{95} +(-23.4342 - 147.957i) q^{97} -1.82056i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39}+ \cdots - 544 q^{97}+O(q^{100}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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